Expanding and Simplifying Polynomial
Expressions
To convert a polynomial expression from factored form to expanded form, use the distributive property:
Some patterns occur frequently and are worth memorizing.
Square of a Sum
Square of a Difference
Difference of Squares
Example 1:
Expand and simplify
.
Solution
Multiply each term in the binomial by each term in the
trinomial. (Distributive Property)
There are 2 X 3 = 6 terms in the expanded form, before
it is simplified.
Collect like terms to simplify the expanded form.
Example 2:
Expand and simplify
Since multiplication is associative, you can
multiply the expressions in any order.
Use the distributive property to multiple.
Drawing arrows help you to keep track of the
multiplications.
1
Mr. White | MHF4U | Unit 0 – Basic Review | Exp. & Simp. Polynomial Exp.
Example 3:
Expand and simplify
Solution
To create less work, use the definition for
Practise:
1. Expand and Simplify
a)
b)
c)
d)
e)
f)
2. Write in simplified expanded form
a)
b)
c)
d)
e)
f)
2
Mr. White | MHF4U | Unit 0 – Basic Review | Exp. & Simp. Polynomial Exp.